Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning

• URL: http://arxiv.org/abs/2605.22263v1
• Date: Thu, 21 May 2026 10:07:46 GMT
• Title: Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning
• Abstract summary: We propose textbfDirection-Adaptive Self-Distillation (textbfDASD), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision.<n>Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines.
• Score: 41.384652481442735
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose \textbf{Direction-Adaptive Self-Distillation} (\textbf{DASD}), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@$k$, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

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